Hi there, not a silly question at all 🙂

You can find information about the WooCommerce REST API here:

https://docs.woocommerce.com/document/woocommerce-rest-api/

as well as the technical documentation here:

https://woocommerce.github.io/woocommerce-rest-api-docs/

In particular:
– specific categories: https://woocommerce.github.io/woocommerce-rest-api-docs/#product-categories
– sale product: https://woocommerce.github.io/woocommerce-rest-api-docs/#product-properties (look for sale_price)

As for recent products, while we don’t have technical documentation for it above, we have a widget and shortcode:
– widget: https://docs.woocommerce.com/document/woocommerce-widgets/#section-1
– shortcode: https://docs.woocommerce.com/document/woocommerce-shortcodes/#section-9